# Maths

Converting a fraction to a decimal
To change a fraction to a decimal, you divide the top number by the bottom number (divide the numerator by the denominator).
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Converting a decimal to a fraction
When you change a terminating decimal to a fraction, the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places).
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Multiples
The multiples of a number are all the numbers that it will divide into. This includes the number itself.For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16
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Simplify algebraic expressions
2x + 5y + x - 3y. Two of the terms involve x, and two involve y.We can re-order the terms in the expression so that the x terms are together and the y terms are together: 2x + x + 5y - 3y. Now combine them together to get 3x+ 2y
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Recipe proportion
Share £200 in the ratio 2:3 This means share the money into 5 equal parts and give one person 2 shares, and the other 3 So 200/5 = 40, one person gets 2 x £40 = £80 and the other 3 x £40 = £120 Check that this adds up to the total, in this case £200
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Pie charts
To draw a pie chart, we need to represent each part of the data as a proportion of 360, because there are 360 degrees in a circle. For example, if 55 out of 270 vehicles are vans, we will represent this on the circle as a segment with an angle of: (
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Dividing in ratio
Share £200 in the ratio 2:3 This means share the money into 5 equal parts and give one person 2 shares, and the other 3 So 200/5 = 40, one person gets 2 x £40 = £80 and the other 3 x £40 = £120 Check that this adds up to the total, in this case £200
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Fractions
9/20 of £360= (£360/ 20) x 9= £162
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Prime numbers
A prime number is a number which doesn't divide into anything else but itself and 1. For example 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
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Interpreting graphs
gradient= change up/ change right or change in / change in x
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Bearings
Find the word from in the question and put your pencil on the diagram at the point you are going from. Draw in a north line where you are going from. Now draw in the angle clockwise from the north line to the line joining the two points
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Scale drawings
Change everything in the same unit. A scale of 1:20 000 would mean that 1 cm is actually equivalent to 200 m
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Area of a rectangle
area= base x height
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Area of a trangle
1/2 × base × height
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Area of a parallelogram
area= base x height
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Area of a trapezium
1/2 × height × (a + b)
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2D shapes
Triangle (3 sides), Quadrilateral (4 sides), Pentagon (5 sides), Hexagon (6 sides) and Octagon (8 sides)
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Regular polygon
A regular polygon has sides that are equal in length and equal angles. A regular triangle is called an equilateral triangle. A regular quadrilateral is called a square.
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Substitution
what is the value of 4p3 when p = 2? We know that 4p3 means 4 × p × p × p, so when p = 2 we substitute this into the expression: 4 × 2 × 2 × 2 (or 4 × 23) = 32
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Percentage increase and decrease
Work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100. If your answer is a negative number then this is a percentage decrease.
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Solving equations
Factorise the quadratic equation x2- 9x + 20 = 0. Find two numbers which add up to 9 and multiply to give 20. These numbers are 4 and 5. (x - 4) (x - 5) = 0. Now find the value x so that when these brackets are multiplied together the answer is 0
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Percentage change
difference/ original x 100
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Circumference of a circle
The circumference is the length of the edge around a circle. Circumference = π x diameter
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Laws of indices
a3 is a short way of writing a x a x
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Right angled trigonometry
sin = opposite / hypotenuse cos = adjacent / hypotenuse tan = opposite / adjacent
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To factorise an expression such x2 + 5x + 6, you need to look for two numbers that add up to make 5 and multiply to give 6. = (x +2) (x+3)
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## Other cards in this set

### Card 2

#### Front

Converting a decimal to a fraction

#### Back

When you change a terminating decimal to a fraction, the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places).

Multiples

### Card 4

#### Front

Simplify algebraic expressions

### Card 5

#### Front

Recipe proportion